I recently sold a Miller GoldStar 300SS welder. It is a very basic three phase stick welder, SCR controlled. Old, big, heavy, simple and bulletproof.
I showed it to the buyer, we did some sample welds from my home three phase, and asked how is he going to use it in his garage.
He said something strange: that he has a friend who is a Union electrician and who said that he can modify it to run from single phase. The buyer said that he is "not an electrician" but he said that his friend sais something about adding a capacitor.
I can imagine, possibly, how he would use just one leg of the three phase transformer, use rectified single phase, and then adding capacitance would somewhat smooth the voltage. But would that not somehow degrade the "constant current" feature of the welder? Maybe producing giant sparks when starting an arc?
The manual of the welder, with schematic, is here: